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Abstract

We numerically and experimentally demonstrate that pulses with a parabolic intensity profile can be formed by passive reshaping of more conventional laser pulses using nonlinear propagation in a length of normally dispersive nonlinear fibre. Moreover, we show that the parabolic shape can be stabilised by launching these pulses into a second length of fiber with suitably different nonlinear and dispersive characteristics relative to the initial reshaping fiber.

Fig. 2. (a) Evolution of the misfit parameter M versus N and ξ. The wave-breaking condition according to Eq. (6) is given by the white solid line. (b) Closer view of Fig. a. Black solid line
joins the points where the optimal parabolic shape is reached. Points 1, 2, 3 4 (circles) represent
the points used in Fig. 1(a), points A, B, C, D (crosses) are used in Fig 3(a) and points I and II (yellow diamonds) correspond to the experimental conditions used in Fig 8 and 12 respectively.

Fig 5. (a) Comparison of intensity profiles of different pulse shape with the same FWHM and the same energy (parabolic pulse are presented in black solid line, other pulses are plotted with the same convention as Fig. 4). (b) Evolution of the misfit parameter M versus N and ξ for a sech pulse.

Fig. 9. (a) Evolution of the misfit parameter M versus N and ξ for an initial Gaussian pulse. The change from N to N’=8 is done when Mopt is reached in the first segment. (b) Evolution of M in the second stage for a parabolic pulse generated in the second stage (solid black line). The results are compared with the evolution a Gaussian (blue line) or sech (red line) pulse of the same FWHM temporal width, same linear chirp and same energy launched in the second fiber.
Inset: intensity profile at the output of the second fiber.

Fig 10. (a) Spectral intensity profiles of the initial Gaussian pulse (grey dotted line) and of the parabolic pulse obtained by numerical simulations at the output of the first segment (N = 2.6, mixed line). Results at the output of the second segment (N’ = 8, ξ = 4) are compared to a parabolic fit. (b) Longitudinal evolution of the FWHM spectral width of the pulse. Numerical results (solid line) are compared with analytical results (blue diamonds).

Fig 11. (a) Influence of the N’ value on the evolution of the misfit parameter Mout at the output of the second segment and on the evolution of the output temporal FWHM. (b) Map similar to the one presented Fig 9(a) but for a sech initial pulse.

Fig. 12. Temporal chirp (top) and intensity (bottom) profiles of the pulses characterized by FROG after the first stage (pink diamonds) and after the second stage (blue circles). Experimental results are compared with parabolic fits (red mixed lines) and with numerical simulations (solid black line).